Question

Consider a play of the casino game `Quick Draw'. In this game, a player pays $11 to play. The player picks one card from a standard pack of 52 cards (i.e. there are four A’s and four K’s in a standard pack of 52 cards). If the player gets an Ace, they win $50 but loose the amount they paid to play (the profit is revenue minus cost); if the player selects a King, they win $30 but loose the amount they paid to play. Otherwise, the player wins nothing and also loses the bet that they placed. Let the random variable X represent the player's profit on a single play of `Quick Draw'. What is the expected value that the player can expect to win each time they play? Answer using two decimals (eg. 2.85)

Answer 1

P(Ace) = P(King) = 4/52 = 1/13

Hence,

Expected value that the player can expect to win

= $(50 - 11)*1/13 + $(30 - 11)*1/13 - $11*11/13

= $ -4.85